Your best bet in all honesty is going to be the brands that will send fitters out (CWD,Devocoux, stubben, county etc.) they will offer a custom fit that can be checked and adjusted regularly (I do yearly if not for often on the young ones)
One that fits. You need to find a good saddle fitter. Best of luck!
Definitely get a professional saddle fitter!
There's not so much a brand as a fit. Obviously the more expensive they are the more padding they'll have, and the softer they'll be, but what matters most is that the saddle fits perfectly, not delivering any uneven pressure. If you aren't 110% certain of your saddle fitting skills, or don't know someone who is, it may be good to get a professional saddle fitter in.
Over time their sensitive back can be helped by strengthening it. You can try stretches everyday like having them turn their necks back to their barrel/hind quarters (which can be accomplished with a treat), having them lift their back (by scratching or talling under their barrel so they lift themselves up), having them stretch their head to the ground (poll pressure) etc...